An Information Theoretic Unified Global Theory For a Stable $M/G/1$ Queue With Potential Maximum Entropy Applications to Energy Works
Ismail A Mageed, Quichun Zhang
Abstract
This paper establishes comprehensive description of the theory of maximum entropy global formalism to analyze a stable <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{M/G/1}$</tex> queue, novel state probability <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{p_{q, UG}(n)},\boldsymbol{n=0,1,}$</tex> 2,… as inductive inference approach for systems. This revolutioanry approach is based on the provision of maximizing Ismail's entropy(IE), namely, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{H_{(q, UG)}}$</tex> , which is the ultimte generalization to all the entropy measures in the literature, subject to prescribed contraints. Numerical portraits are provided to capture the influential effect of the derived formalism, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{p_{q, UG}(n),\ n=} \boldsymbol{0,1,2, \ldots}$</tex> on the stable <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{M/GE_{q, UG}/1}$</tex> queue with heavy tails. An expxposition to several potential applictaions of maximum entropy(ME) to energy works is undertaken. Conclusion with possible future research pathways are given.